Due to its advantages of having a high power-to-weight ratio and being energy-efficient, the electro-hydraulic servo pump control system (abbreviated as EHSPCS) is frequently employed in the industrial field, such as the electro-hydraulic servo pump control (EHSPC) servomotor for steam turbine valve regulation control. However, the EHSPCS has strong nonlinearity and time-varying features, and the factors that cause system performance degradation are complex. Once a system failure occurs, it may lead to serious accidents, causing serious casualties and economic losses. To address the above issues, a system health assessment method based on LSTM-GRNN-ANN (LGA) deep neural network is proposed in this paper. Firstly, with oil volume gas content, servo motor air-gap flux density, and system leakage coefficient as the health assessment performance indicators, a health assessment performance index system for the EHSPCS is built, Furthermore, the system performance index threshold is set. Secondly, an LGA deep neural network is constructed by combining LSTM, GRNN and ANN, and a deep neural network based on the LGA is used to create an EHSPCS health assessment model. Subsequently, system feature parameter extraction, algorithm design, and parameter debugging are carried out. Finally, an EHSPCS experimental platform is established, typical system failure simulation experiments are designed, and comparative experimental analysis is conducted. The experimental findings demonstrate that the average accuracy of the system health assessment model based on the LGA deep neural network suggested in this paper is 96.37%, compared to 89.84%, 87.99% for LSTM and GRNN, which validates the accuracy of the system health assessment model based on the LGA deep neural network.